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  • Market Equilibrium with Private Knowledge: An Insurance Example

    Kunreuther, H.C. and Pauly, M.V.

    IIASA Working Paper


    June 1982

  • Kunreuther, H.C. and Pauly, M.V. (1982) Market Equilibrium with Private Knowledge: An Insurance Example. IIASA

    Working Paper. IIASA, Laxenburg, Austria, WP-82-058 Copyright © 1982 by the author(s).

    Working Papers on work of the International Institute for Applied Systems Analysis receive only limited review. Views or

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    Howard Kunreuther Mark Pauly

    J u n e 1 9 8 2 WP82-58

    Working Papers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute or of its National Member Organizations.





    I n s u r e r ' s P o t e n t i a l S t r a t e g i e s S t a b i l i t y of E q u i l i b r i u m W e l f a r e E f f e c t s


    N a t u r e of E q u i l i b r i u m An I l l u s t r a t i v e E x a m p l e O b t a i n i n g V e r i f i e d I n f o r m a t i o n






    Howard Kunreuther and Mark Pauly


    The effect of asymmetric information between buyers and sellers on

    product quality was first explored by Akerlof (1970) in his pathbreaking

    paper on the market for "lemons." He showed that if all purchasers have

    imperfect information on quality, then a market for the product may not

    exist, or if it does function it may not be efficient. These results have led

    to a number of papers concerning insurance and labor markets under dif-

    ferent assumptions regarding how agents discriminate between "pro-

    'The research reported in this paper is partially supported by the Bundesrninisterium f i k Forgchung und Technologic, F.R.G., contract no. 321/7501/RGB 8001. While support for this wark is grateiully acknowledged, the views expressed are the authors' own m d are not neces aarily shared by the sponsor. We are gratetul to Zenan Fortuna and Serge Medow for compu- tational assistance and to David Cummins and Peyton Young and the participants in the Conference on Regulation of the International tnstitute of Management, Berlin, July, 1081, especially Jdrg Rnsinger and Paul Kleindorfer. for helpful comments and suggestions. An earlier version of this paper is included in the conference proceedings.

  • ducts" of varying quality. (See Pauly 1974, Rothschild and Stiglitz 1976,

    Wilson 1977, Miyasaki 1977, and Spence 1978).

    These treatments assume that all of the imperfectly informed agents

    have identical levels of knowledge of product quality. In contrast, this

    paper will consider situations where some agents learn over time about

    the quality of a particular good. However, this knowledge is private or

    agent-specific and may be costly for others to obtain. For example, firms

    may learn about the differential skills of their labor force by observing

    their productivity; other firms do not have easy access to this informa-

    tion. Insurance firms learn about the risk characteristics of their custo-

    mers by observing claims records; they will not share these data cost-

    lessly with their competition. We are interested in characterizing the

    nature of the market equilibrium when agents have such private

    knowledge on the endowed qualities of a good. Our analysis is undertaken

    in the context of insurance markets, although it is applicable to those

    situations where sellers cannot easily communicate their product's spe-

    cial qualities to prospective buyers even though the current purchasers

    have a t least partially observed these features.

    The following problem is first analyzed in detail. Suppose that a set

    of customers has been with a specific insurance firm for t years, durmg

    which time the firm has collected information on their claims experience.

    The insurer naturally will not make these data available to other firms,

    and consumers are unable to furnish verified hstories. Not having direct

    knowledge of each customer's risk class, the insurance firm utilizes

    claims data to set premiums. What is the schedule of profit-maximizing

    rates at which no customer will have an incentive to purchase insurance

  • elsewhere in period t + l?

    We consider two polar cases with regard to the assumption made

    about firm behavior. In one case, we assume that the firm has n o

    j w e s i g h t , so that it sets prices to make non-negative expected profits in

    every period. In the other, we assume that the firm has p e r f e c t fo re s igh t ,

    in the sense that it maximizes the present discounted value of the

    expected profit stream over the planning horizon. We assume in each

    case that consumers choose the firm making the most attractive offer in

    the current period. In this paper, consumers do not have the foresight to

    consider the stream of premiums that will be charged in the current

    period and all future periods. This assumption therefore represents one

    polar case, with perfect consumer foresight models such as those of

    Dionne (1981), Radner (1981), and Rubinstein and Yaari (1980) a t the

    other extreme.

    We refer to the situation in which neither firm nor customers have

    foresight as s ing le - per iod equi l ibr ia , since firms can change their price

    from one period to the next and consumers are free to stay or leave as

    they see fit. We refer to the situation in whch firms maximize &scounted

    expected profits but consumers choose only on the basis of current

    period premiums as m y o p i c m u l t i - period equ i l i b r ium. 2

    The paper is organized as follows. We first begin at the end, so to

    speak, by considering in Section I1 a static model in whch the firm

    currently selling insurance to individuals has perfect private knowledge

    'one of the purposes of experience rating is to cope with problems of moral hazard. This pa- per does not answer the question as to whether a premium adjustment process ce.n eliminate or substantially reduce moral hazard. The paper also does not consider the possibility of re- quiring individuals to state their probability of loss and using experience to "punish" those who misstate (cf. Radner 1881, Rubinstein and Yaari 1880).

  • about each person's risk class. We show how the premiums charged are

    nevertheless constrained by other insurance firms. Section 111 develops a

    model in which firms use i . o rma t ion from the claims experience of the

    insured in a Bayesian fashion to adjust individual premiums to experi-

    ence. We show that in the single-period equilibrium model, the resulting

    premium schedule yields positive expected profits and monopoly distor-

    tions even if entry by new firms into the market is completely free. Profit

    or rate regulation would be a natural remedy if reality approximated this

    equilibrium. We further consider briefly the impact on the single period

    equilibrium of permitting customers to buy verified information on their

    experience. This would include purchase of data on premium classifica-

    tions or claim records.

    Section lV shows that in a myopic multi-period equilibrium, expected

    profits are zero with free entry, but price distortions remain. Premiums

    are generally below expected costs in the early periods, but eventually

    rise to exceed expected costs. The concluding section suggests applica-

    tions and extensions of the analysis.


    Our world consists of two types of consumers. Every consumer faces

    the possibility of an identical single loss (x) whch is correctly estimated

    and which is independently distributed across individuals. Each consu-

    mer of type i has a probability of a loss Q i , i = H , L for the high and low

    risk group respectively ( a H > a L ) . The consumers correctly perceive

    these values of Qi. The proportion of h g h and